Question

From the top of a cliff 100 m high, the angles of depression of the top and the bottom of a tower are observed to be ${30}^{\circ }$ and ${60}^{\circ }$, respectively. The height of the tower is

• A. 66.7 m
• B. 56.8 m
• C. 23.7 m
• D. None of these

Answer 1

The correct option is A 66.7 m


$tan{60}^{\circ }=\frac{100}{AB}=\frac{100}{EC}$
Or $EC=\frac{100}{\sqrt{3}}$
$tan{30}^{\circ }=\frac{100-h}{EC}$
Or $EC=(100-h)\sqrt{3}$
Or $\frac{100}{\sqrt{3}}=(100-h)\sqrt{3}$
Or $100=300-3h$
$\Rightarrow h=\frac{200}{3}=66.7m$